Solve frac{sqrt{3}x}{1}-frac{sqrt{2}}{1}frac{3sqrt{6}}{7}=frac{2sqrt{3}}{1}

$$\frac{ \sqrt{ 3 } x }{ 1 } - \frac{ \sqrt{ 2 } }{ 1 } \frac{ 3 \sqrt{ 6 } }{ 7 } = \frac{ 2 \sqrt{ 3 } }{ 1 }$$

Solve for x

$$x = \frac{20}{7} = 2\frac{6}{7} \approx 2.857142857$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 7.

$$7\sqrt{3}x-\sqrt{2}\times 3\sqrt{6}=7\times 2\sqrt{3}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$7\sqrt{3}x-\sqrt{2}\times 3\sqrt{2}\sqrt{3}=7\times 2\sqrt{3}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$7\sqrt{3}x-2\times 3\sqrt{3}=7\times 2\sqrt{3}$$

Multiply 2 and 3 to get 6.

$$7\sqrt{3}x-6\sqrt{3}=7\times 2\sqrt{3}$$

Multiply 7 and 2 to get 14.

$$7\sqrt{3}x-6\sqrt{3}=14\sqrt{3}$$

Add 6\sqrt{3} to both sides.

$$7\sqrt{3}x=14\sqrt{3}+6\sqrt{3}$$

Combine 14\sqrt{3} and 6\sqrt{3} to get 20\sqrt{3}.

$$7\sqrt{3}x=20\sqrt{3}$$

Divide both sides by 7\sqrt{3}.

$$\frac{7\sqrt{3}x}{7\sqrt{3}}=\frac{20\sqrt{3}}{7\sqrt{3}}$$

Dividing by 7\sqrt{3} undoes the multiplication by 7\sqrt{3}.

$$x=\frac{20\sqrt{3}}{7\sqrt{3}}$$

Divide 20\sqrt{3} by 7\sqrt{3}.

$$x=\frac{20}{7}$$